Question 1

Which of the following relations is a function?

Accepted Answer

$$\{(0,1), (1,2), (2,3)\}$$

Question 2

Given the graph of $$y = x^2$ for x$$ \in [-2,2]$$, what is the domain and range in interval notation?

Accepted Answer

Domain: $$[-2,2]$$, Range: $$[0,4]$$

Question 3

Which of the following graphs passes the vertical line test and is therefore a function?

Accepted Answer

A parabola opening upwards

Question 4

Given the piecewise function $$f(x) = \begin{cases} 4 & x \u003c 3 \ x^2$ - 3 & 3 \leq x \u003c 8 \ x^3$ & x \geq 8 \end{cases}$$, what is $$f(-1)$$?

Accepted Answer

$$4$$

Question 5

A real-world scenario: The cost $$C(x) to $$rent a car is given by $$C(x) = \begin{cases} 30 & 0 \leq x \leq 1 \ 30 + 20(x-1) & x \u003e 1 \end{cases}$$, where $$x is $$the number of days rented. What is the cost to rent the car for 3 days?

Accepted Answer

$$70$$

Question 6

Which of the following is the correct interval notation for the domain of the function $$f(x) = \sqrt{x-2}$$?

Accepted Answer

$$[2, \infty)$$

Question 7

Given the piecewise function $$f(x) = \begin{cases} x+1 & x \leq 1 \ x^2$ & x \u003e 1 \end{cases}$$, what is $$f(1)$$?

Accepted Answer

$$2$$

Question 8

A function $$f is $$defined as $$f(x) = 2x + 3. $$What is the range of $$f$$?

Accepted Answer

$$(-\infty, \infty)$$

Question 9

Which of the following best describes a piecewise function?

Accepted Answer

A function defined by multiple equations for different intervals of $$x$$

Question 10

Given the relation $$\{(2,5), (0,2), (2,9)\}$$, is this a function? Why or why not?

Accepted Answer

No, because the input 2 is paired with two different outputs

Question 11

If a graph has a domain of $$[-4,5]$$ and a range of $$[-1,2]$$, which of the following is the correct interval notation for the range?

Accepted Answer

$$[-1,2]$$

Question 12

Suppose $$f(x) = \begin{cases} 2x+4 & x \u003c 0 \ x^2$ & 0 \leq x \u003c 2 \ x^2$ + 5 & x \geq 2 \end{cases}. $$What is $$f(2)$$?

Accepted Answer

$$9$$

Question 13

A function $$g is $$defined as $$g(x) = \frac{1}{x-1}. $$What is the domain of $$g$$?

Accepted Answer

$$(-\infty, 1) \cup (1, \infty)$$

Question 14

Which of the following real-world scenarios can be modeled by a piecewise function?

Accepted Answer

A cell phone plan that charges a flat rate for the first 100 minutes and a per-minute rate after that

Question 15

Given the function $$f(x) = x^2$ - 3x + 2$$, what is the range of $$f$$ for $$x \in [0,3]$$?

Accepted Answer

$$[0,2]$$

Question 16

If a function $$f is $$not defined for $$x=2$$, which of the following could be its domain?

Accepted Answer

$$(-\infty, 2) \cup (2, \infty)$$

Question 17

Which of the following statements is true about the range of a function?

Accepted Answer

The range is the set of all possible output values

Question 18

Given the piecewise function $$f(x) = \begin{cases} -4 & x \u003c -2 \ x+1 & -2 \leq x \u003c 1 \ x^2$ & x \geq 1 \end{cases}$$, what is $$f(0)$$?

Accepted Answer

$$1$$

Question 19

A function $$h is $$defined as $$h(x) = \sqrt{5-x}. $$What is the range of $$h$$?

Accepted Answer

$$[0, \infty)$$

Relations, Functions, Domain & Range, and Piecewise Functions: Calculus Foundations

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